Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format

Maolin Che (), Juefei Chen () and Yimin Wei ()
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Maolin Che: Southwestern University of Finance and Economics
Juefei Chen: Fudan University
Yimin Wei: Fudan University

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 5, 852-877

Abstract: Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples.

Keywords: Tensor CUR decomposition; Low multilinear rank approximation; Maximal volume sub-matrices; Mode-n unfolding; Tucker decomposition; 15A18; 65F10; 65F15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02051-w

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